>>7811655
You can't find the surface of a rectangle?

>>7811664
More like i can't reach the summation equation to proof the equation

Dx is n. That should get you started. As noted approaches inf

>>7811683
What is the width of each rectangle?
1/n
What is the height of the k-th rectangle?
(k/n) ^3 +1

You just need to sum for the possible values of k

>>7811717
Yes, this. Use r instead of k to see how OPs pic applies.

Is [math]\int x^3+1\,dx[/math] acceptable, or would you write
[math]\int (x^3+1)\,dx[/math]?
I think I'd do the latter.